MAT 189 is open to other majors only with permission of instructor. All students must have completed at least 24 units in upper division mathematics courses (above 100). The target audience is seniors (very advanced juniors with permission of instructor).

The aim of this course is to have students use all that they have learned during their studies within a single quarter-long project that brings together topics covered in the academic courses in their particular major.
This course is unlike any other at our program, as students are exposed to a role played by mathematicians in solving large problems (not just homework sets!) and how mathematical thinking is translated into action. The course will lead students to make connections in their course knowledge and to fill gaps when necessary. The students will develop skills for communicating mathematics, both in writing and verbally, in formal and informal environments.

The course will be graded with the project, oral presentations, and various drafts. There will be a few exercises and quizzes along the way.

References: The following resources will be used (the prices of these resources are very affordable). NONE is required for purchase.

As a capstone class this course will put to use and test many of the skills learned in prior courses.

For many undergraduates, this is the first chance to write a long-term project (7 weeks to prepare and develop) and to do real advanced research (REU style). Students also have oportunities to write rigorous proofs and how to clearly deliver mathematical thinking orally. Students work in teams to solve challenging problems testing and honing their abilities to work in groups.

Prerequisite and Expectations

Students need at least 24 upper division units completed prior to Spring quarter (100 level or above). This class targets seniors or very advanced juniors, as it is a capstone course. Depending on the project, some knowledge of programming is required.
Formal attendance will not be taken. However, whether you are able to attend class or not, you are responsible for all the material presented in class. Moreover you are expected to report weekly progress on your project to the professor.
This is a 3 unit course. You are expected to work 3 hours at home for each hour of hour of lecture. In other words, expect to have 10 hours of duties each week.

Syllabus

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Lecture(s)	Sections	Comments/Topics
Week 1		Lectures 1, 2 & 3: Choosing a good capstone project, examples of (realistic) projects and how to choose a project. Guidelines for effective research. Discussion possible areas of exploration suitable for undergraduates (examples of past projects, suggestions cover all areas of mathematics and its applications, 15 different projects discussed). During first week students select a project with help from professor. Student will form teams (roughly 3 students each) and together develop the project. Here are some past areas of research (relevant courses are indicated): Check below for current offering. Mathematics of elections and dividing things fairly.(135AB,145,168,167,133, 160) Mathematical problems arising in Sports and Games.(145,168,167,160,135AB) Mathematical problems Scheduling, planning, and information (148,135AB,145,160,168,133) The art of solving equations (150ABC,115AB,128ABC, 165,119,118) Graph theory challenges (145,146,148,150) <\li> Combinatorial Geometry and Topology (141,114,145,147,116,146) Mathematics and Art (111,141,125AB, 150ABC,115AB, 129) Investigating Polynomials and their properties (150,125,135AB,165,141) Clusters and patterns in data (114,168,167) Other topics? Only with approval of professor! WARNING: Decisions on projects must be finalized no later than lecture 3. Students will begin giving oral presentations to all the group on what they will do.
Week 2		Lecture 4: General guidelines for giving technical or scientific oral presentations (e.g, time, design of slides, content organization, how to organize a blackboard presentation). Introduction to LaTEX slides, powerpoint. How to prepare a Poster. Teaching mathematics and talking to non-mathematicians. Lecture 5: General guidelines for good writing (Strunk and White). Discussion of Zinsser' book that explores the idea of writing as way of learning. Good writing reflects/helps clear thinking. Guidelines for Mathematical & Scientific writing guidelines. Lecture 6: Students officially start on their projects today. Presentations will begin, maximum of 5 slides. More on using LaTEX. Using Mathscinet, ZentralBlatt, BIBTEX (bibliographic tools).
Week 3		Lecture 7: Students oral presentations in front of class, describing their projects. Lecture 8: Students oral presentations in front of class describing their projects. Lecture 9: Students oral presentations in front of class describing their projects.
Week 4		Lecture 10: Selected advanced topics from Mathematical Sciences that may help on projects (see sources). Relation to undergraduate mathematics coursework at UCD and how topics interrelate. Lecture 11: Selected advanced topics from Mathematical Sciences that may help on projects (see sources). Relation to undergraduate mathematics coursework at UCD and how topics interrelate. Lecture 12: Selected advanced topics from Mathematical Sciences may helpon projects. Relation to undergraduate mathematics coursework at UCD and how topics interrelate. IMPORTANT: First written Draft of project due today (end of fourth week). Students exchange papers and will receive comments from each other and from professor.
Week 5 (halfway)		Lecture 13: Problem solving strategies and how to develop a project. What is a proof and methodologies one can use to arrive to one. Lecture 14: Problem solving strategies and how to develop a project. What is a model and the role of data and computers? Tools of applied Mathematics. Lecture 15: Problem solving strategies and how to develop a project.
Weeks 6		Lecture 16: Discussion on careers in the mathematical sciences. Networking for jobs. Lecture 17: Guest lecture from industry, discussion on non-academic jobs. Lecture 18: Graduate school: is it for you? IMPORTANT: Second draft version of projects due today.
Weeks 7		Lecture 19: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. Lecture 20: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. Lecture 21: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. IMPORTANT: Third draft version of projects due today.
Weeks 8		Lecture 22: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. Lecture 23: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. Lecture 24: Professor+TA lead workshop on revising fine tuning projects. Meetings with individual students in class. IMPORTANT: All students hand in fourth draft version of their projects. Last round of comments prior to final presentations/final version.
Weeks 9,10 & Finals-week.		Final presentations begin continue until finals week (max 25 minutes long per presentation). TA and Professor hear evaluate the presentations using rubric. Students expected to attend some presentations besides their own.

Grading:
The grades will be calculated using the average and standard deviation of the class. 100 points are possible which will be divided as follows:

Four drafts- 30 points (10 points each, but lowest score dropped),
Four Quizzes or writing exercises (5 points each, lowest dropped),
Final Project report 30 points (Due June 13th),
Final presentation slides (15 points), and
Oral presentation (10 points)

Some important rules will be followed:

Your work is not being graded solely from the correctness of the answer. We expect you to write clean well-structured prose, justify your reasoning and show all details.
The drafts you submit should be free of mispellings and have a high standard of composition and organization.
The final project should be done without help (only mine and the TA's)
Students are able to drop Math courses on their own until Friday, April 20, 2015 (20th day of instruction)

SOFTWARE and other RESOURCES:

Some projects may use expensive software such as MATLAB, SCIP, LaTEX, etc. You do not have to buy such software. You have several options for accessing the software:

To create an account at the Math Department. Visit http://www.math.ucdavis.edu/comp/class-accts and follow the instructions.

It is important to create your account if you are in need of software. You can then work either at the Undergraduate Computer Lab (2118 Math. Sci. Bldg.) or from any other lab in the campus or even from your home PC by remotely connecting to one of the departmental servers, such as [point,cosine,sine,tangent].math.ucdavis.edu. The lab is open 9am-5pm on weekdays.

IMPORTANT: KEY INFORMATION ABOUT PROJECTS

A list of available projects and details of the final project's format and style are available here

HOMEWORK 1

Write a one-slide description of yourself in latex, by Friday April 10th class. Here is the template example I showed in class. SUBMISSION via email to me, before class!!

Advanced Problem Solving: Capstone course

IMPORTANT: KEY INFORMATION ABOUT PROJECTS

HOMEWORK 1